Rewrite as a simplified fraction. ${2.\overline{92} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 292.9292...\\ 1x &= 2.9292...\end{align*}}$ Subtracting the two equations, we have: ${99x = 290}$ ${x = \dfrac{290}{99}} \text{or} {2 \dfrac{92}{99}}$